The commission counted over 99 percent of the vote as of 2:00 a.m. local time on Monday (GMT 1:00 AM). No candidate is close to receiving more than 50 percent of the vote.
According to the latest data, Milanovic has 29 percent of the vote, followed by Grabar-Kitarovic at 26 percent. Entrepreneur Miroslav Skoro is slightly behind the incumbent president with 24 percent of the vote.
Zoran Milanovic, 53, the nation's former prime-minister, was reportedly forecast to win in the first round of the presidential vote, according to polls cited earlier by local media during the election campaign.
The remaining candidates are polling far behind, according to preliminary commission data.
A runoff is slated for 5 January 2020.
The Croatian head of state has, to a large extent, a ceremonial role. The president cannot veto bills but has a say in foreign policy and defence issues. The president has a five-year term, with the next one starting in February 2020.